A certain medical test is known to detect 72% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

Question

Mathematics

Raphael

11 August, 23:00

A certain medical test is known to detect 72% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?

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Answers (1)

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Adyson · Answer 1

Answer: 10773

Step-by-step explanation:

.75^10=0.0563

look at 8, 9, 10

8 the probability is 10C8*0.75^8*0.25^2=0.2816

9 the probability is 0.1877 using the same approach

At least 8 is 0.5256

At most 4 is

0.25^10=essentially 0

1: 10C1*0.75*0.25^9=<0.0001

2: 45*0.75^2*0.25^8=0.0004

3: 120*0.75^3*0.25^7=0.0031

4: 10C4*0.75^4*0.25^6=0.0162

That sum is 0.0197